This work was published very recently (March 24, 2013) in Nature.  The below paper was a release from a few months earlier.  I have no connection with this work.  A friend, R. Wagner, brought this to my attention.

GaAs is an expensive material,  but it gives higher efficiencies than Si and other more conventional solar cell materials. The use of the nanowires as was done in this study potentially reduces the needed amount of GaAs material by 100 to 10,000 fold.   So I would say this looks to be a major breakthrough toward low cost high efficiency solar.

Single nanowire solar cells beyond the Shockley-Queisser

limit

Peter Krogstrup1,*, Henrik Ingerslev Jørgensen2,*, Martin Heiss3,*, Olivier

Demichel3, Jeppe V. Holm2, Martin Aagesen2, Jesper Nygard1, Anna Fontcuberta i

Morral3,†

1 Center for Quantum Devices, Nano-Science Center, Niels Bohr Institute, University of Copenhagen,

Denmark

2SunFlake A/S, Nano-Science Center, Universitetsparken 5, DK-2100 Copenhagen, Denmark

3 Laboratoire des Matériaux Semiconducteurs, Ecole Polytechnique Fédérale de Lausanne, 1015

Lausanne, Switzerland

*equal contribution

Light management is of great importance to photovoltaic cells, as it determines

the fraction of incident light entering the device. An optimal pn-junction

combined with an optimal light absorption can lead to a solar cell efficiency

above the Shockley-Queisser limit. Here, we show how this is possible by

studying photocurrent generation for a single core-shell p-i-n junction GaAs

nanowire solar cell grown on a silicon substrate. At one sun illumination a short

circuit current of 180 mA/cm2 is obtained, which is more than one order of

magnitude higher than what would be predicted from Lambert-Beer law. The

enhanced light absorption is shown to be due to a light concentrating property of

the standing nanowire as shown by photocurrent maps of the device. The results

imply new limits for the maximum efficiency obtainable with III-V based

nanowire solar cells under one sun illumination.

Nanowire based solar cells hold promise for third generation photovoltaics and for

powering nanoscale devices.1,2 In the avenue of third generation photovoltaics, solar

cells will become cheaper and more efficient than current devices, in particular a cost

reduction may be achieved by the possibility of rationalizing the material use through

the fabrication of nanowire arrays and radial p-n junctions.3,4,5 The geometry of

nanowire crystals is expected to favour elastic-strain relaxation, giving a major

freedom for designing new compositional multi-junction solar cells6 grown on

mismatched materials.7,8 Till today, the efficiencies of nanostructured solar cells have

indeed been increasing with time up to 10%, owing to the improvement of material

and device concepts.9,10,11,12,13,14

Light absorption in standing nanowires is a complex phenomenon, with a strong

dependence on the nanowire dimensions and absorption coefficient of the raw

material.15,16,17,18In low absorbing micro-wire arrays such as Si, light absorption is

understood via ray optics or by the calculation of the integrated local density of

optical states of the nanowire film.19,20Interestingly, when these arrays stand on a

Lambertian back reflector, an asymptotic increase in light trapping for low filling

factors is predicted.19 This is advantageous for the improvement of the efficiency-tocost

ratio of solar cells and has led to the demonstration of micro-wire arrays

exhibiting higher absorption than the equivalent thickness textured film19,21,22Quite

different is the case of nanowires whose diameters are smaller than or comparable to

the radiation wavelength. In this case, optical interference and guiding effects play a

dominating role on the reflectivity and absorption spectra. For low absorbing

materials (such as indirect bandgap, Si) wave-guiding effects plays a key role23,24

while highly absorbing semiconductors (such as direct bandgap, GaAs) exhibit

resonances that increase the total absorption several-fold. Nanowires lying on a

substrate also exhibit such resonances, often described by Mie theory,25,26 though the

total absorption rate is significantly lower.27,28 Even though optical absorption in

nanowires pertaining to an array has shown to be far more complex than in thin films,

nanowire vertical arrays seem to be the most reasonable device proposal nowadays.

An elegant device consists in a single standing nanowire solar cell, contacted on top

by a transparent electrode and at the bottom through the substrate. While the

characterization of single nanowires lying on a substrate is quite common, until today,

there are no studies on standing single nanowires.

In this work we present experimental measurements on single GaAs nanowire solar

cells as grown on a silicon substrate where the p-part is contacted through a highly

doped substrate and n-part with a transparent top-contact (see figure 1a-c and ref 26).

We find that light absorption in single standing nanowires is more than one order of

magnitude more efficient than what would be predicted from Lambert-Beer law. We

show measurements on two devices. The first device (figure 1) exhibits a short circuit

current density of 180 mA/cm2, when normalized to the projected area. This leads to

an apparent solar conversion efficiency of 40%. The second device shows a short

circuit current of 173mA/cm2 and an apparent efficiency of 28%. The reason for these

very high efficiencies is the mismatch between the absorption cross-section and the

physical bounds of the nanowires, hinting at a very large absorption cross section.

This work represents a critical step towards the next generation of nanowire based

solar cells.

Current-voltage characteristics of the devices were measured in the dark and under

AM 1.5G illumination. Experimental data of device 1 are shown in Fig. 1d. In the

dark, the device exhibits typical diode behaviour with an ideality factor of 2.6. Under

illumination, the diode curve is shifted downwards as a consequence of the photo4

generation and separation of electron-hole pairs, giving a short-circuit current of 256

pA. The diameter of the nanowire is 425 nm corresponding to an apparent photogenerated

current density of 180 mA/cm2. The open circuit voltage Voc and fill-factor

FF are respectively 0.43 V and 0.52, which should be improved by optimizing the

resistivity, thickness of the doped layers and surface passivation.29 The generated

power at the maximum power point is 57 pW, corresponding to 40 mW/cm2. Dividing

the generated power density by the incident power density, the solar cell yields an

apparent efficiency of 40%. In order to understand the extreme photon collection

boost in free standing single GaAs nanowires, we use finite difference time domain

method to model a 2,5 μm long nanowire embedded in SU-8 as a function of its

diameter and of the wavelength of the plane wave radiation propagating along the

nanowire axis.30,31,32 In figure 2a, the wavelength and diameter dependence of the

absorption rate of such a nanowire is shown. Note that the absorption is zero for

wavelengths larger than 900 nm where the absorption coefficient of GaAs goes down

to zero. Two dominant branches for low and high diameters are observed,

corresponding to resonances similar to Mie resonances observed in nanowires lying

on a substrate25. Light absorption in the standing nanowire is enhanced by a factor

between 10 and 70 with respect to the equivalent thin film. Another way to express

this enhancement in absorption is through the concept of an absorption cross-section.

The absorption cross-section is defined as Aabs = an where a is the physical crosssection

of the nanowire and n is the absorption efficiency. It is largely accepted that

the absorption cross-section in nanoscale materials is larger than their physical size. In

systems such as quantum dots, the absorption cross-section can exceed the physical

size by a factor of up to 8.33 We have calculated the absorption cross-section of the

nanowires as a function of the nanowire diameter and incident wavelength (Fig. 2b).

The absorption cross-section is in all cases larger than the physical cross-section of

the nanowire. It is interesting to note that the absorption of photons from an area

larger than the nanowire itself is equivalent to a build-in light concentration, C. Light

concentration has an additional benefit that it increases the open circuit voltage with a

term kTlnC and thereby increasing the efficiency.34,35, 36 The largest absorption cross

section in figure 2b is 1.13x106 nm2 at a nanowire diameter of 380 nm

(a=9.38x104nm2), corresponding to an overall built-in light concentration of about 12.

Measurements of the external quantum efficiency (EQE) normalized by the physical

area for both lying and standing nanowire devices are shown in figure 3a (see

supplement for more details). Lying nanowires exhibit EQE values up to 2 due to Mie

resonances37, while for standing nanowires values of up to about 14.5 are reached.

This further confirms that the absorption cross-section is several times larger than the

apparent cross section of the wire, especially at wavelengths close to the bandgap.

To further understand the absorption boost in our devices, we have spatially mapped

the photocurrent generated by a vertical nanowire device for three different excitation

wavelengths: 488, 676 and 800 nm. The results presented in Figures 3b-d are

deconvoluted with the point spread function of the diffraction limited laser spot. As

seen in the figure a photocurrent from an area much larger than the size of the laser

spot appears for all three wavelengths. A fit to the data allows estimating an effective

absorption cross-section diameter of 1.2 μm (488 nm), 1.0 μm (676 nm) and 1.3 μm

(800 nm) respectively. Hence, the absorption boost in our device is due to an

unexpected large absorption cross-section of the vertical nanowire geometry. This is

equivalent to a built-in light concentration of about 8, which is in good agreement to

what our theory predicts. In addition, we speculate that the top contact geometry

further contributes to the resonant absorption effect, thereby increasing the absorption

cross-section and the boost in photo-generated current. 3839

Finally, we put our results in perspective by comparing them to top-notch existing

technologies and with the design principles for increasing efficiency. In Table 1 we

have listed the record values for leading technologies such as single junction

crystalline silicon and GaAs, as well as triple junction devices. The highest efficiency

is obtained by the triple-junction solar cell (34.1%), with a short-circuit current of

14.7 mA/cm2. In this case, the short-circuit current is maintained relatively low, as it

has to be matched between the three cells connected in series and what gives the high

efficiency is the increase in Voc. The highest short-circuit current is obtained in a

crystalline silicon (c-Si) solar cell, where light management techniques resulted into

the boost of photo-generated current of 42.7mA/cm2. The record efficiency recorded

by Alta Devices with GaAs was obtained with a relatively thin film, few microns in

contrast to few hundred microns in standard cells. This brings us to the discussion of

what determines high efficiency. A solar cell operates at a voltage that maximizes the

generated power, dictated by the values of the short-circuit current, FF and Voc.

Design towards higher efficiencies points to strategies for increasing these values.40,41

The first two parameters concern mainly the device ‘engineering’ , while the ultimate

Voc is dictated by the thermodynamics of the solar energy conversion into electrical

work. Within the Shockley-Queisser model, Voc is limited by the following terms:36

where T and Tsun are the temperature of the cell and of the sun respectively, Ωemit and

Ωsun correspond to the solid angle of emission and collection, n the refractive index of

the material and QE is the emission quantum efficiency. The first term is related to

the Carnot efficiency, which reduces Voc by ~5%. The second term corresponds to the

entropic losses occurring in the work generation. The first entropy loss is due to the

non-reciprocity in the angle of light absorption and emission. Light resonant

structures such as nanowires can reduce the contribution of this term.36 The second

entropy loss takes account of the concentration factor, given by the refractive index

and any external concentration: Voc increases by implementing light trapping

strategies, with the additional benefit of increasing absorption close to the

bandgap.42,43 The last entropic term refers to the non-radiative losses. It can be

reduced to zero by increasing the QE to 1. The impressive result on GaAs cells by

Alta Devices was obtained thanks to increasing QE in a GaAs thin film to 1. Our

results provide a further path for higher efficiency solar cells. Even though the

electrical characteristics shown are not ideal yet, we observe a light concentration

effect plus the significant increase of absorption rate close to the bandgap, similar to

what is proposed by ref 36. These two effects are so that nanowire structures can

reduce entropy in the conversion of solar energy into electrical work, thereby

providing a path for increasing efficiency of solar cells. It is also important to note

that the unexpected increase in the absorption cross-section enables to further separate

the nanowires from one another, resulting in major cost reductions of the final device.

Our experiments indicate that a good inter-wire distance would be around 1.2 μm. A

nanowire solar cell consisting of nanowires similar to the device showed in Fig 1

positioned in a hexagonal array with a pitch of 1 μm (optical cross-section with a

diameter of ~1.2 μm) would have an optical filling-factor of 1 and it would only use

an equivalent material volume of a 546 nm film and exhibit a conversion efficiency of

4.6%. Using devices with smaller area, see left branch from Fig. 1, one could further

reduce the amount of material used up to a factor 72. By improving the electrical

characteristics of the pn junction, higher efficiencies could be obtained. Just

considering an effective light concentration of 15, an array of GaAs nanowires with

ideal characteristics would exhibit an efficiency of 33.4% , hereby overcoming the

Shockley-Queisser limit for the planar GaAs solar cells illuminated by 1.5AM

radiation, according to the discussion presented above34,44 Even higher efficiencies

could be achieved if the device design could be tailored for higher light concentration

and QE. Note that axial junctions, which have the same junction area as the projected

area would obtain the full benefit from such concentrator effect, and it would be

possible to directly compare performance of GaAs nanowire solar cells under 1 sun

with planar GaAs cells under 10 suns. We demonstrate here that single nanowire

devices generate several-fold higher power than their projected area convey when

they are standing upright, which also minimizes their footprint. It should be pointed

out that if one were to build a single nanowire solar cell, then a flat lying nanowire

would exhibit ~15 times lower power density compared to the standing nanowire

device due to the light concentration effect. This enhancement in the energy

conversion at the nanoscale makes them useful as energy harvesters with minimum

footprint feeding other devices on the same chip. This is already the case for nanowire

based pn junctions with non-ideal characteristics like the one shown in this work. Last

but not least, the improvement in the photon collection renders them in general ideal

as photo-detectors.

In conclusion, we have observed a remarkable boost in absorption in single nanowire

solar cells that is related to the vertical configuration of the nanowires and to a

resonant increase in the absorption cross-section. These results open a new avenue for

third generation solar cells, local energy harvesters on nanoscale devices and photon

detectors.

Methods:

Nanowire growth. Nanowires were grown on an oxidized (111) Si with 100 nm

apertures using a self-catalysed method. Ga nominal growth rate was 900nm/h,

substrate temperature 630oC and V/III ratio 445,46. P-doping of core was achieved by

adding a flux of Be during axial growth47. Cores were annealed for 10 min at 630oC.

The shell was obtained at 465oC, growth rate of 300 nm/h and with a V/III ratio of 50.

N-type doping was obtained by adding Si to the growth.

Device fabrication and characterization. SU-8 was spun-on the substrate at

4000rpm for 45s and cured with 1min UV light and 3min on a hotplate at 185oC.

Then an etch-back with 1-3min oxygen plasma etch was performed to free the

nanowire tip. The top contact was defined by e-beam lithography followed by

evaporation of indium-tin-oxide (more details can be found in supplementary

information). The bottom contact was obtained by silver glueing to the back-side of

the wafer. Current-voltage characteristics were measured in the dark and under 1.5G

conditions with a standard solar simulator (LOT – Oriel 150W Xe lamp) with a 1”

beam diameter and an AM1.5G filter. Photocurrent map of the devices were collected

by scanning the contacted sample under the laser spot focused with a 63x and 0.75

N.A. lens.

Finite Difference Time Domain method simulations. The absorption of standing

2.5 μm GaAs nanowires of different diameters standing on silicon and surrounded by

SU-8 was calculated by solving Maxwell equations in three dimensions for an

incident plane wave radiation normal to the substrate. The wave equation is solved in

time domain following refs 30 and 27.

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Acknowledgements:

This research has been funded by the ERC starting grant UpCon, by SNF through

projects nr 137648, 143908 and NCCR-QSIT. AFiM thanks STI for the 2011 end-ofyear

fund for MiBoots robots used in the scanning photo-current experiment. AFiM

and MH thank Anna Dalmau-Mallorqui and Franz Michael Epple for experimental

support. We thank Claus B. Sørensen and Morten H. Madsen for assistance on MBE

growth. This work was supported by the Danish National Advanced Technology

Foundation through project 022-2009-1, a University of Copenhagen Center of

Excellence, and by the UNIK Synthetic Biology project.

Author contribution:

PK grew the nanowire pn junctions. HIJ did the I-V characterisation and fabricated

the device with help from JVH and MA. MH and OD performed the FDTD

calculations. MH realized the photocurrent mappings and the external quantum

efficiency measurements. AFiM and PK conceived and designed the experiments.

AFiM, JN and MA supervised the project. AFiM, HIJ, PK and MH made the figures

and wrote the manuscript. All authors discussed the results and commented on the

manuscript.

Author information:

Correspondence and requests for materials should be addressed to anna.fontcubertamorral@

epfl.ch or krogstrup@fys.ku.dk.

Figure 1. Electrical characterization of a single nanowire solar cell (device 1). a.

Schematic of the vertical single nanowire radial p-i-n-device connected to a p-type

doped Si wafer by epitaxial growth, b Left: Doping structure of the nanowire. The ptype

doped core is in contact with the doped Si substrate and the n-type doped shell is

in contact with the ITO is illustrated. Right: A typical SEM image of a nanowire

from the same growth with a 30o angle from the vertical c Scanning electron

micrographs of the device seen from the top electrode. The nanowire is ~2.5 μm high

and has a diameter of about 425nm. d Current voltage characteristics of the device in

the dark and under AM 1.5G illumination, showing the figure of merit characteristics.

Figure 2. Optical simulations of a single nanowire solar cell. Simulations on the

light absorption in a 2.5 μm standing GaAs nanowire that is fully embedded by

SU-8 (n=1.67) on a Si substrate: the absorption rate of solar AM1.5G radiation in a

and simulated absorption cross-section in b exhibit two main resonant branches,

similar to Mie resonances observed in nanowires lying on a substrate. The periodic

modulation with wavelength is a result of Fabry-Pérot interference in the polymer

layer and not an artifact of the simulation.

Figure 3. . Optical characterization of a single nanowire solar cell (device 2). a.

External quantum efficiency (EQE) normalized by indicated projected area where

vertical and horizontal nanowire solar cells are compared. As seen for the vertical

standing solar cell a 15 fold increase in the photon collection is obtained close to the

bandgap. The EQE becomes negligible for photon wavelengths below the bandgap of

GaAs, meaning that there is no contribution from absorption in the Si substrate47 (bd)

Scanning photocurrent measurements on our single vertical nanowire device for

three different excitation laser wavelengths, normalized to the incident photon flux.

The scale bar corresponds to 1 μm.

Table1. Short-circuit current (JSC), fill-factor, open-circuit voltage, area and

efficiency of top-notch photovoltaic technologies compared with the standing

nanowire configuration presented in this work. The low Voc and FF values indicate

the potential for improvement of the nanowire cell presented, see text below for

discussion (*apparent efficiency calculated with the projected area of the cell).